Abstract: Knowledge inference on knowledge graph has attracted extensive attention, which aims to find out connotative valid facts in knowledge graph and is very helpful for improving the performance of many downstream applications. However, researchers have mainly poured attention to knowledge inference on binary facts. The studies on n-ary facts are relatively scarcer, although they are also ubiquitous in the real world. Therefore, this paper addresses knowledge inference on n-ary facts. We represent each n-ary fact as a primary triple coupled with a set of its auxiliary descriptive attribute-value pair(s). We further propose a neural network model, NeuInfer, for knowledge inference on n-ary facts. Besides handling the common task to infer an unknown element in a whole fact, NeuInfer can cope with a new type of task, flexible knowledge inference. It aims to infer an unknown element in a partial fact consisting of the primary triple coupled with any number of its auxiliary description(s). Experimental results demonstrate the remarkable superiority of NeuInfer.